Hundreds of Turkish citizens also lined up outside election board offices in Ankara and Istanbul on Tuesday, to submit petitions requesting the board to reverse its declaration following the referendum results.
If the referendum results are recognised by the parliament, the president will have sweeping new executive powers in almost all branches of the state including in the government, the military and in the monetary policies, unlike any other president over the past century.
The vote allows Erdogan, who has ruled Turkey first as prime minister and now as president since 2003, to fulfill his long-held ambition for a presidency with executive powers.
Trump telephoned Erdogan on Monday to "congratulate" him on "his referendum victory" and to discuss last week's US cruise missile strike on Syria and cooperation in the campaign there against the Islamic State, a White House statement said. "We will demonstrate a democratic resistance, we will use all democratic means to be able to keep this issue alive and we will let this issue be debated in public so as not to give any easy blessing to the government that this whole package [of constitutional amendments] has been adopted orderly", Yilmaz said.
Those protests were sparked by plans to uproot trees in Istanbul's Gezi Park to build a shopping mall.
Thousands have been protesting in major cities since Sunday's referendum, which has set into motion the transformation of Turkey's system of government from a parliamentary to a presidential one.
She vowed that her party will "not recognise" the referendum result, arguing that the referendum process was fraudulent and the results were manipulated.More news: Trump to order review of national monuments
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Turkey's Supreme Election Board (YSK) rejected appeals to annul the referendum results after a meeting on Wednesday.
The board met for seven hours Wednesday before rejecting the request.
In response, CHP Deputy Chairman Bulent Tezcan said his party was considering taking its appeal to Turkey's Constitutional Court or the European Court of Human Rights.
"As a result of evaluations, the appeals were rejected with 10 votes against and 1 vote in favour", it said in a statement.
Turkey's top electoral board is considering objections Wednesday to the way the country's referendum was run, according to Turkey's semi-official Anadolu news agency.
Metin Feyzioglu, head of the Union of Turkish Bar Associations, said the decision to count unstamped ballots, without keeping any record of them, removed the main safeguard against voting fraud.
Yildirim said the opposition parties have the right to file objections, but "calling people to the street is wrong and is outside the line of legitimacy", Yildirim said, telling CHP leader Kemal Kilicdaroglu to "to act more responsibly".